I want to place a Wasabi DX modchip in a new Wii family edition. But there's a D4 drive in it, is it posible to replace the entire drive with a D2B model and place the modchip on that one?
Or will there be a problem with the drive because there are no GC ports on the Wii?

AFAIK, you should be able to swap in a D2B drive with a modchip. If you're planning on connecting the Wasabi Zero via the drive cable, it will be limited to 3x read speed just like a softmod, so there's not much of an advantage over a softmod. A wired install will allow full 6x read. Any reason why you don't want to go softmod and USB loading? There's little reason to use discs at this point.